Find the DE that is consistent with this method

**Borkborkmath** · June 10th 2012, 11:58 AM

How do I find a DE that is consistent with:

$u_j^{n+1}=\frac{1}{2}(u_{j+1}^n+u_{j-1}^n)-\frac{1}{2}\frac{\Delta t}{(\Delta x)^3}(u_{j+2}^n-2u_{j-1}^n-u_{j-2}^n)$

Also, when is the scheme stable?

**BobP** · June 10th 2012, 12:34 PM

Are you sure about that $(\Delta x)^{3}$ ?

**Borkborkmath** · June 10th 2012, 01:03 PM

Yes I am :\

**BobP** · June 11th 2012, 12:52 AM

Too bad, $(\Delta x)^{2}$ and I could probably offer some help. I'm not familiar with methods involving $(\Delta x)^{3}$ .

**Borkborkmath** · June 11th 2012, 11:18 AM

can you offer your help for the x^2? And I'll see what I can do to change it for x^3?

**BobP** · June 12th 2012, 12:00 AM

It's just textbook stuff. Look at the section on the solutions of parabolic equations.

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